展開する (-xcos^2(y)-xsin^2(y))^2

解

展開する

(- x cos^{2} (y) - x sin^{2} (y))^{2}

x^{2} cos^{4} (y) + 2 x^{2} cos^{2} (y) sin^{2} (y) + x^{2} sin^{4} (y)

解答ステップ

(- x cos^{2} (y) - x sin^{2} (y))^{2}

完全平方式を適用する:

(a - b)^{2} = a^{2} - 2 ab + b^{2}

(- x cos^{2} (y) - x sin^{2} (y))^{2} = (- x cos^{2} (y))^{2} - 2 (- x cos^{2} (y)) x sin^{2} (y) + (x sin^{2} (y))^{2}

= (- x cos^{2} (y))^{2} - 2 (- x cos^{2} (y)) x sin^{2} (y) + (x sin^{2} (y))^{2}

簡素化

(- x cos^{2} (y))^{2} - 2 (- x cos^{2} (y)) x sin^{2} (y) + (x sin^{2} (y))^{2} : x^{2} cos^{4} (y) + 2 x^{2} cos^{2} (y) sin^{2} (y) + x^{2} sin^{4} (y)

= x^{2} cos^{4} (y) + 2 x^{2} cos^{2} (y) sin^{2} (y) + x^{2} sin^{4} (y)